a) \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{5^{10}.9^{10}.5^{20}}{5^{15}.5^{15}.3^{15}}=\frac{5^{30}.3^{20}}{5^{30}.3^{15}}=3^5=243\)
b) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{2^3.3^3+3.2^2.3^2+3^3}{-13}\)
\(=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=-3^3=-27\)
c) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\frac{2.6}{3.5}=\frac{4}{5}\)
d) \(\frac{3.11+42}{5^3}=\frac{33+42}{5^3}=\frac{75}{5^3}=\frac{5^2.3}{5^3}=\frac{3}{5}\)
Câu a là 243
Câu b là -27
Câu c là 4 phần 5
câu d là 3 phần 5
